IMO 2008 Shortlist N4

Let n be a positive integer. Show that the numbers  2n − 1  ,  2n − 1  ,  2n − 1  , ... ,  2n − 1 2n−1 − 1  are ...

imomathematicsolympiadshortlistnumber-theory

IMO 2008 Shortlist N4

Category: Number Theory

Problem

Let n be a positive integer. Show that the numbers  2n − 1  ,  2n − 1  ,  2n − 1  , ... ,  2n − 1 2n−1 − 1  are congruent modulo 2n to 1,3,5,...,2n −1 in some order.